I wonder why uncertainties in angle measurement MUST be in radians.
For example, I want to calculate the uncertainty in measuring the function $y= \sin (\theta)$ when the angle is measured $\theta = 63$ $\pm 1$ degree. I do this using differential, so $dy = \cos (\theta) d\theta$, now $d\theta = \pm 1$ degree is the error in $\theta$. Now, all the course notes/ books I read says this must be converted in radians, even though the angle we use here is measured in degree. How come?
Thanks
Cal2
Best Answer
Because, if you don't use radians the derivative of $\sin\theta$ is not $\cos\theta$, and so your formula $dy=\cos\theta\,d\theta$ doesn't hold (it needs a coefficient).